Birth-death processes with mass annihilation and state-dependent immigration

A birth-death process is subject to mass annihilation at rate β with subsequent mass immigration occurring into state j at rateα j . This structure enables the process to jump from one sector of state space to another one (via state 0) with transition rate independent of population size. First, we highlight the difficulties encountered when using standard techniques to construct both time-dependent and equilibrium probabilities. Then we show how to overcome such analytic difficulties by means of a tool developed in Chen and Renshaw (1990, 1993b); this approach is applicable to many processes whose underlying generator on E\{0} has known probability structure. Here we demonstrate the technique through application to the linear birth-death generator on which is superimposed an annihilation/immigration process.

Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration

Attention has recently focussed on stochastic population processes that can undergo total annihilation followed by immigration into state j at rate αj. The investigation of such models, called Markov branching processes with instantaneous immigration (MBPII), involves the study of existence and recurrence properties. However, results developed to date are generally opaque, and so the primary motivation of this paper is to construct conditions that are far easier to apply in practice. These turn out to be identical to the conditions for positive recurrence, which are very easy to check. We obtain, as a consequence, the surprising result that any MBPII that exists is ergodic, and so must possess an equilibrium distribution. These results are then extended to more general MBPII, and we show how to construct the associated equilibrium distributions.

Constructive trusts, illegal purpose and locus poenitentiae

Analyses the Family Division decision in Q v Q on the competing claims of a father and son to beneficial ownership of a house in which the father sought to on a secret agreement entered into with his sons when transferring the property into their joint names, intended to subvert the inheritance tax rules on lifetime gifts by retaining the right to have the property transferred back to him, and the son relied on a later agreement with his brother to transfer the house into his sole name, in reliance on which he and his wife had acted to their detriment by paying for its upkeep and renovation.

The M/M/1 queue with mass exodus and mass arrivals when empty

An M/M/1 queue is subject to mass exodus at rate β and mass immigration at rate {αr; r≥ 1} when idle. A general resolvent approach is used to derive occupation probabilities and high-order moments. This powerful technique is not only considerably easier to apply than a standard direct attack on the forward p.g.f. equation, but it also implicitly yields necessary and sufficient conditions for recurrence, positive recurrence and transience.

Embedding dynamic behaviour into a self-configuring software system

This paper describes a methodology for embedding dynamic behaviour into software components. The implications and system architecture requirements to support this adaptivity are discussed. This work is part of a European Commission funded and industry supported project to produce a reconfigurable middleware for use in automotive systems. Such systems must be trustable against illegal internal behaviour and activity with external origins, additional devices for example. Policy-based computing is used here as an example of embedded logic. A key contribution of this work is the way in which static and dynamic aspects of the system are interfaced, such that the behaviour can be changed very flexibly (even during run-time), without modification, recompilation or redeployment of the embedded application code. An implementation of these concepts is presented, focussing on achieving trust in the use of dynamic behaviour.

Rats, floods and flowers: London's Gothicized nature

AUTHOR's OVERVIEW This chapter attempts a definition of London eco-gothic, beginning with an ecocritical reading of the ubiquitous London rat. Following Dracula, popular London gothic has been overrun, from the blunt horror-schlock of James Herbert’s 1970s Rats series to China Miéville’s King Rat. Maud Ellman’s elegant discussion of the modernist rat as a protean figure associated with a ‘panoply of fears and fetishes’, underlines how the rat has always featured in anti-urban discourse: as part of racist representations of immigration; as an expression of fear of disease and poverty; or through a quasi-supernatural anxiety about their indestructible and illimitable nature which makes them a staple feature of post-apocalyptic landscapes. Even so, the London rat is a rather more mundane manifestation of urban eco-gothic than the ‘city wilderness’ metaphors common to representations of New York or Los Angles as identified by eco-critic Andrew White. London’s gothic noses its way out through cracks in the pavements, grows from seeds in suburban gardens or accumulates through the steady drip of rainwater. However, I will suggest, in texts such as Maggie Gee’s The Flood and P. D. James’ Children of Men, London eco-gothic becomes less local and familiar as it responds to global environmental crisis with more dramatic tales of minatorial nature.

Raman spectroscopy in pharmaceutical analysis

A wide and versatile range of analytical techniques are routinely used, indeed are necessary, in pharmaceutical analysis. Over the past decade Raman spectroscopy has increasingly come to the fore as a valuable member of the arsenal of methods used, from both a fundamental and applied perspective, for the interrogation of solid, liquid and solution phase samples. Advances have occurred not only in instrumentation but also in fundamental techniques and applications. The method holds substantial potential for the investigation of, what are normally considered, problematic or challenging areas of analysis. The aforementioned areas include – but are, definitely not limited too reaction kinetics, pharmaceutical drug discovery, detection of counterfeit/adulterated/illegal drugs, trace analysis and uses for on-line pharmaceutical process manufacturing. This, the first of several articles on the use of Raman spectroscopic techniques in pharmaceutical analysis, provides an introductory overview of the theory of the technique.